Abstract

In this paper, we define the q-analog Virasoro-like Lie subalgebras in x∞ = a∞(b∞, c∞, d∞). The embedding formulas into x∞ are introduced. Irreducible highest weight representations of , , and -series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the , , , and -series of the q-analog Virasoro-like Lie algebras.

Received 18 May 2012Accepted 28 February 2013Published online 20 March 2013

Acknowledgments:

This work is supported in part by the National Science Foundation of China (NSFC) (Grant Nos. 10931006 and 11101269), the Innovation Program of Shanghai Municipal Education Commission (11ZZ18) and the Fundamental Research Funds for the Central Universities.

Article outline:I. INTRODUCTIONII. VERTEX OPERATOR REPRESENTATIONS OF III. EMBEDDING INTO a∞ AND THE , , -SERIES OF A. The caseB. The caseC. The caseIV. VERTEX OPERATOR REPRESENTATION OF THE LIE ALGEBRAV. VERTEX OPERATOR REPRESENTATION OF THE LIE ALGEBRAVI. POLYNOMIAL REPRESENTATIONS